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Police in Texas fear a serial bomber planted four powerful explosive devices that have killed two people and injured four others this month, raising fears in the state capital Austin of another attack.

Investigators said they have no clear idea what motivated the series of attacks, which began 17 days ago, and have publicly reached out to the bomber, urging him or her to contact them and explain his demands.

The first three devices were parcel bombs dropped off at night in front of homes on the city's east side, with the fourth a trip wire device that went off in a west side neighborhood on Sunday. All four devices were similar, police said on Monday.

"We are clearly dealing with what we expect to be a serial bomber at this point," Brian Manley, Austin Police Chief, told a news conference near the site of Sunday's bombing.

The men, 22 and 23 years old, were taken to a hospital with what police described as "substantial" but not life-threatening injuries.

Mr Manley said more than 500 federal agents were involved in the investigation, including from the Federal Bureau of Investigation and U.S. Bureau of Alcohol, Tobacco, Firearms and Explosives.

"There is an army of law enforcement folks on the scene right now," Steve Adler, the city's mayor, said on CNN. "I am confident that we're going to find whoever is responsible for this and then we're going to stop it."

FBI agents have swept the relatively affluent neighbourhood called Travis Country where Sunday's bomb exploded and asked residents for home surveillance videos.

"It's scary," Thad Holt, a 76-year-old retiree, said in an interview, recalling that he and his wife had strolled near the bomb site about half an hour before the explosion. "It's one of those things ... that happens elsewhere."

Austin, with a population of nearly 1 million people, is home to the University of Texas and a plethora of tech companies and has been one of the fastest growing major U.S. cities.

The first bombing, on March 2, killed Anthony Stephan House, a 39-year-old black man. It ripped a hole in a home entrance wall and damaged the front door.

Austin police have asked the bomber or bombers to contact them and explain the motivation behind the attacks.

"The person is actually trying to provoke fear and that is made worse by simply not giving information about why," said Robert Pape, an international security expert and director of the University of Chicago Project on Security and Threats.

APD is asking the public to remain vigilant and report anything suspicious. If you come across ANYTHING that looks suspicious, DO NOT touch, handle or disturb it. Keep a safe distance and call 9-1-1 immediately. pic.twitter.com/buJsLqeRy5